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Acta Physica Sinica

Propagation of optical pulses through one-dimensional photonic crystals with a dispersive and gain defect layer

Yu Tian-Bao, Nian-Hua Liu, 南昌大学物理系,南昌 330047

Published Jan 1, 2004• 2 citations
Publisher

Abstract

The propagation of a pulse through onedimensional photonic crystals with a dispersive and gain defect layer is discussed. The dispersion and gain of the defect layer is described by Lorentz oscillator model. It is found that the pulse pea k exhibits subluminal and superluminal behaviors with varying strength of the os cillator. The Poynting vector and energy velocity can be negative, but the latte r is never faster than the vacuum light speed c. The advance or delay of the pulse peak is a result of the coherent superposition of all Fourier components which experienced different phase shift and different amplification in the medium.

DOI
10.7498/aps.53.3049

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The propagation of a pulse through onedimensional photonic crystals with a dispersive and gain defect layer is discussed. The dispersion and gain of the defect layer is described by Lorentz oscillator model. It is found that the pulse pea k exhibits subluminal and superluminal behaviors with varying strength of the os cillator. The Poynting vector and energy velocity can be negative, but the latte r is never faster than the vacuum light speed c. The advance or delay of the pulse peak is a result of the coherent superposition of all Fourier components which experienced different phase shift and different amplification in the medium.
The propagation of a pulse through one-dimensional photonic crystals that contain a dispersive and absorptive defect layer doped with two-level atoms is discussed. The dynamical evolution of the pulse inside the photonic crystal is presented. Superluminal negative group velocity (the peak appears at the exit end before it reaches the input end) is discovered. Although the group velocity is larger than c and even negative, the velocity of energy propagation never exceeds the vacuum light speed. The appearance of the superluminal advance or subluminal delay of the pulse peak inside the photonic crystal or at the exit end is due to the wave interference from Bragg reflections.
We discuss the light pulse propagation in a one-dimensional photonic crystal doped by graphene quantum dots in a defect layer. The graphene quantum dots behave as a three-level quantum system and are driven by three coherent laser fields. It is shown that the group velocity of the transmitted and reflected pulses can be switched from subluminal to superluminal light propagation by adjusting the relative phase of the applied fields. Furthermore, it is found that by proper choice of the phase difference between applied fields, the weak probe field amplification is achieved through a one-dimensional photonic crystal. In this way, the result is simultaneous subluminal transmission and reflection.
Pulse propagation through 1-dimensional stratified media is studied. The general features of pulse propagation in relation to the delay or advancement of the pulse are discussed. It is shown that in a lossless system with spatial symmetry the reflected and the transmitted pulses have the same delay or advancement. The phase times and the explicit output pulse profiles for an input Gaussian pulse are calculated. While recalling recent results for a variety of systems (resonant absorbers or heterogeneous medium in a Fabry-Perot cavity, a slab of negative index medium, a left-handed/right-handed periodic structure, etc.), new results involving coupled waveguides and a high finesse cavity containing an electromagnetically induced transparency (EIT) medium are presented. Calculations clearly show that for pulses with a carrier tuned at the resonance of the stratified media, one generally has subluminal propagation. Alternatively, in stop gaps or away from the resonances one ends up with superluminal transit. In the case of the EIT cavity it is shown that the large dispersion offered by the intracavity medium can lead to substantial superluminality (ng≃−106) with peak transmission as high as 20%. This is in sharp contrast to large signal attenuation for usual superluminal transit. Note also that EIT, to the best of the authors knowledge, has so far been used to achieve only slow light.
The propagation of pulses through dispersive media was investigated by solving Maxwell's equations without any approximation. We show that the superluminal propagation of pulses through anomalous dispersive media is a result of the interference of different frequency components composed of the pulse. The coherence of the pulse plays an important role for the superluminal propagation. With the decrease of the coherence of the pulse, the propagation changes from superluminal to subluminal. We have shown that the anomalous dispersion (the real part of the susceptibility) not the amplification (the imaginary part of the susceptibility) plays the essential role in the superluminal propagation. Although the superluminality always exists as long as the spectrum of the coherent pulse is within the anomalously dispersive region, both the energy propagation velocity and the frontal velocity never exceed the light speed in the vacuum. The output pulse through the medium is not the original pulse; instead it carries the information of the original pulse and the information of the prepared medium.